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Chapter 8: Problem 8

Solve each of the given equations for \(x .\) Check your answers by hand or with a calculator $$4 x-10=-2 x+8$$

Short Answer

Expert verified
Answer: The solution for the linear equation is \(x = 3\).

Step by step solution

01

Simplify and collect like terms on both sides of the equal sign

Add \(2x\) to both sides of the equation to bring all of the \(x\) terms to one side: \(4x - 10 + 2x = -2x + 8 + 2x\) This simplifies to: \(6x - 10 = 8\)
02

Isolate the variable \(x\)

Add \(10\) to both sides of the equation to remove the constant term on the left side: \(6x - 10 + 10 = 8 + 10\) This simplifies to: \(6x = 18\) Now, divide both sides of the equation by \(6\) to isolate \(x\): \(\frac{6x}{6} = \frac{18}{6}\) This simplifies to: \(x = 3\)
03

Check your answer

Check the solution by substituting \(x = 3\) back into the original equation: \(4(3) - 10 = -2(3) + 8\) This simplifies to: \(12 - 10 = -6 + 8\) And further simplifies to: \(2 = 2\) Since both sides of the equation are equal, that means our solution of \(x = 3\) is correct.

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